Problem: Solve for $x$ and $y$ using elimination. ${-2x+2y = -12}$ ${5x-2y = 39}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $3x = 27$ $\dfrac{3x}{{3}} = \dfrac{27}{{3}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-2x+2y = -12}\thinspace$ to find $y$ ${-2}{(9)}{ + 2y = -12}$ $-18+2y = -12$ $-18{+18} + 2y = -12{+18}$ $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ You can also plug ${x = 9}$ into $\thinspace {5x-2y = 39}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ - 2y = 39}$ ${y = 3}$